Pole-Swapping Algorithms for Alternating and Palindromic Eigenvalue Problems

Vietnam Journal of Mathematics(2020)

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摘要
Pole-swapping algorithms are generalizations of bulge-chasing algorithms for the generalized eigenvalue problem. Structure-preserving pole-swapping algorithms for the palindromic and alternating eigenvalue problems, which arise in control theory, are derived. A refinement step that guarantees backward stability of the algorithms is included. This refinement can also be applied to bulge-chasing algorithms that had been introduced previously, thereby guaranteeing their backward stability in all cases.
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关键词
Eigenvalue,QZ algorithm,Palindromic pencil,Alternating pencil,Pole swapping
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